Problem: The sum of two numbers is $34$, and their difference is $8$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 34}$ ${x-y = 8}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 42 $ $ x = \dfrac{42}{2} $ ${x = 21}$ Now that you know ${x = 21}$ , plug it back into $ {x+y = 34}$ to find $y$ ${(21)}{ + y = 34}$ ${y = 13}$ You can also plug ${x = 21}$ into $ {x-y = 8}$ and get the same answer for $y$ ${(21)}{ - y = 8}$ ${y = 13}$ Therefore, the larger number is $21$, and the smaller number is $13$.